Question

A marketing study found that the mean spending in 15 categories of consumer items for 150 respondents in the 18 to 34 age group was RM75.50 with a standard deviation of RM53.20. For 250 respondents in the 35+ age group, the mean and the standard deviation were RM65.20 and RM46.10, respectively. Test the hypothesis that there is no difference in the mean spending between these two populations. Use a significance level of 0.05. (Note: Assume that the population variances are not equal)

Answer 1

	Age 18to34 (1)	Age 35+ (2)
n	150	250
Mean	75.5	65.2
SD	53.2	46.1

v1 = n1 - 1 and v2 = n2 -1

We have to test for the equality of the two population means assuming no equal variacnes. Since we have n > 30 and the populations are independent we will use the t-test for independent samples.

We have to test for the difference not if greater or less so the test is two tsiled.

p-value = 2* P(t_df >| Test Stat|)

Where P(t_df >| Test Stat|) is found using t-dist tables.

Null
Alternative
Null difference	0
Test Stat	1.9688
df	280
p-value	0.04996	P(t280 > 1.97)=0.0249
Since p-value < 0.05
Decision	Reject the null hypothesis.
There is sufficiet evidence at 5% to conclude a difference between the two means.